一种基于弱拟牛顿方程的对角拟牛顿法  

A Diagonal-Sparse Quasi-Newton Method Based on Weak Quasi-Newton Equation

作　　者：鲍莹莹[1] 王希云[1] 程翠梨[1] 

机构地区：[1]太原科技大学应用科学学院,山西太原030024

出　　处：《宁夏师范学院学报》2013年第3期15-19,共5页Journal of Ningxia Normal University

摘　　要：基于弱拟牛顿方程,结合Armijo非精确线性搜索设计了一种求解大规模无约束优化问题的对角拟牛顿法,该算法在每次迭代时利用对角矩阵逼近Hessian矩阵,使计算搜索方向的存储量和工作量明显减少.在一定的假设条件下,证明了算法的全局收敛性和R-线性收敛性.通过数值实验表明该算法是有效的,适于求解大型无约束优化问题.Based on weak Quasi-Newton equation ,we propose a diagonal-sparse Quasi-Newton method for unconstrained opti- mization problems. The method uses Armijo＇ s line search rule to define a step-size at each iteration. In the method Hessian matrix was approximated by diagonal matrix, reducing the computation and storing space. In given conditions,we prove global convergence and R- linear convergence. Numerical results also show that the new method is efficient and suitable for solving large scale optimization problems.

关 键 词：无约束优化 弱拟牛顿方程 对角拟牛顿法 全局收敛性 线性收敛性 

分 类 号：O221[理学—运筹学与控制论]